CHAPTER IV — Critical Commentary & Notes

On Round Columns with Their Bases, Capitals, and Pedestals or Stylobates, and How the Corinthian Capital and Its Four Tetrants Are Constructed.

Historical & Mathematical Commentary

  • Paganini 1509 Plate Referenced: Folio 0213 (0213.rst, 0213.g1.png) shows the complete Corinthian/Ionic column on its stylobate and stereobate with all the reference letters (\(a, b, c, d, e, f, g, h, k, l, m, n, o, p\)) cited in Cap. IV–Cap. VI.

  • Exact Arithmetic of :math:`frac{1}{8} - frac{1}{10} = frac{1}{40}`: Notice how Pacioli expresses the thickness of the abacus as the difference between the two Vitruvian human head ratios from Cap. III—the whole head (\(\frac{1}{8}\)) minus the face (\(\frac{1}{10}\)), which equals \(\frac{1}{40}\) (the crown of the skull from hairline to vertex!).

Philological and Folio Apparatus

  • 1509 Paganini Witness Folios: 0069, 0070 (f. 27r–f. 27v)

  • Winterberg 1889 Italian Source: winterberg/02_architectura_italian/004_cap_IV.txt

  • Winterberg 1889 German Source: winterberg/04_architectura_german/004_cap_IV.txt

  • Marginal Woodcut Diagrams: 0 figure(s) extracted from the 1509 Venice witness.